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In this scene from the film, Gravity, the main characters are informed that

... a debris field traveling faster than a high speed bullet ...

Yet they can see the debris approaching just moments later. The debris is approaching slow enough that Lt. Matt Kowalski can visually identify a disabled satellite.

Satellites orbiting the Earth such as the Space Shuttle make one orbit every 90 minutes and cover a circumference of about 40,000 kilometers. This works out to about 445 kilometers per minute. That comes to 7.416 kilometers per second, not about 10 meters per second as shown in the movie. And much faster than a high speed bullet, which is 1.5 kilometers per second.

How could they see something moving 5 times faster than a bullet?

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    The debris field may be moving at one velocity - but the individual debris will be moving at all sorts of velocities following the collision (and the field will eventually spread out). – HorusKol Jan 9 '17 at 2:28
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    Also - the shuttle may be travelling at 7.4 km/s relative to the ground - how fast is the debris travelling at relative to the ground? and what is it's vector relative to the orbit of the shuttle? that will affect the approach speed between the shuttle and the debris field. – HorusKol Jan 9 '17 at 2:30
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    This question is not off-topic, as it is asking for an explanation of an in-universe phenomena. It just so happens that they can (hopefully) be explained using Newtonian mechanics. – Gallifreyan Jan 9 '17 at 8:56
  • @HorusKol Yes, there would be a range of velocities for individual debris pieces, so wouldn't the pieces arriving first be those traveling the fastest? And if those are traveling the fastest, wouldn't those be the hardest to see? – RichS Jan 14 '17 at 18:18
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You actually can't see a bullet mainly due to size. Upgrade it to something bigger and it's another story. For example:

The talk is about debris - you can say that this satellite chunk that misses Lt. Kowalski is a big one. The bigger they are the easier they are to spot...

Another important bit is that in space there is no atmosphere so visibility is much better. Thus you can see much smaller things much farther out than on Earth. This is, BTW, the reason why space-borne telescopes don't have to be as big as the ground-side ones to yield images in much higher resolution and quality.

EDIT: after reading some comments I think It's time to add some info.

First of all it's incorrect to assume all satellites travel at same speed, same altitude and in same direction. For example Hubble's period is about 95 minutes, which would translate to about 9 km/s (32000 km/h). Hubble also, probably, is in sun-synchronous orbit (slightly retrograde) brackets, meaning it travels in a huge pack of other satellites, passes another bunch or two on its way each revolution. Debris in question came from satellite hit by a missile, which turned into a debris cloud travelling upwards at the speed of 32000 km/h (according to data in the video). However, this is a spy satellite (which means LEO, which means about 400-450 km of distance between the two orbits). Missile strike obviously imparted some of it's speed on the debris itself (added or detracted, depending on the exact orbit) and depending on the direction from the missile came it could significantly change the vectors. And we're talking about MULTIPLE satellites...

In other words: all those factors may represent huge velocity difference as a result. Different inclination, different orbit period, tangential motion... all adds up.

EDIT 2: And by "it's all adding up" i mean this: russians bungled it up enormously by using missile (from POV of orbital safety). Usually satellites are disposed by burning them in the atmosphere (where possible) to avoid the situation exactly as shown in the movie. Go to stuffin.space to see just how chock full of stuff the Earth orbit is. from NASA appraisals majority of that stuff is in 0-100 kg range, meaning pretty heavy projectile. But back to destroyed satellite. Using missile means intercept trajectory, not pursuit (fuel limitations and depending on the location of the interceptor's launch big-to-severe speed penalty). Successful interception means change in speed (it will be significantly reduced) and trajectory of the debris (as mentioned in the movie: "upward"). Since we have around 2300 satellites overhead, with most of them in similar orbit, inclination and period (and other stuff - hopefully I'm using right words), there will be a chain reaction. Each "succesfully" destroyed satellite will create it's own debris cloud, and each time some of the debris will be moving slower than before and more and more "upward" (i.e. away from Earth). Repeat it multiple times and in the end we have this situation: Shuttle, traveling at his nominal speed, enters the debris field which moves across his trajectory much slower and at an angle. This would be the equivalent - to use Nathan's cool analogy of a car from comments below - of running red light during a traffic jam at a high speed Since the russian satellite almost certainly was moving slower than the shuttle to start with (as it being "probably spy sat", to the tune of the "low-to-mid speed bullet"), now difference in speed is staggering.

As far as the OP question goes: satellite is usually the size of a human being. How far out can you see human being? On Earth it's about 6 km (curvature and atmosphere get in the way), in space it can be much farther (but, admittedly, due to eye limitations as a speck of reflected sunlight and without the ability to gauge distance from it until much bigger).

Disclaimer: always when speed is used with no other qualificators it's meant to be speed relative to Earth

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    Also because although the debris is going 7.5 km/s, so are they, meaning that their difference in speed will be negligible. – user205186 Jan 9 '17 at 12:24
  • No. Basic Newtonian physics - what you think of would be a situation when objects travel at same speed in the same direction, thus they are motionless in relation to each other. And this would also mean the damage from hit would be minimal. We know - just from the linked movie fragment - that this was not the case.. – AcePL Jan 9 '17 at 12:41
  • The answer lies somewhere in between the two comments above I think. The debris is not travelling at the speed of a bullet relative to the shuttle, and is large enough and relatively slow enough to be visible prior to impact, however the relative impact speed is still high enough to cause damage. e.g. if I throw a brick at the rear window of a stationary car it will smash the window. If the car is moving away from the brick then the brick will appear to be moving more slowly from the cars perspective. The brick will still damage the car though, if it's moving fast enough to hit it. – Nathan Griffiths Jan 11 '17 at 0:56
  • @Nathan - but your comment predicates on few assumptions that are incorrect. But let's start with this one: debris cloud expands hitting a bunch of satellites. Each time it SLOWS DOWN. So what we have in the video could be thesituation equivalent to brick thrown straight up, ending - with it at it's apogeum (that is being motionless relative to brick thrower) - directly in the path of the fighter jet... So you're right it comes down to relative motion, but missing on the other conditions having impact on the final effect. – AcePL Jan 11 '17 at 10:14
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    @AcePL you don't seem to have explained what assumptions you think I've made that are incorrect and I don't think your analogy makes sense. But staying on topic to the original question I think we are in agreement that the characters can see the debris because it's relative speed to the characters is less than its relative speed to the Earth. – Nathan Griffiths Jan 11 '17 at 23:57

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